First some background … my original post used a video clip from "Stand and Deliver" to map the information flow in the traditional classroom. I also used the illustration below (from "Math Is Language Too: Talking and Writing in the Mathematics Classroom" by Phyllis Whitin) to demonstrate how students learn to "do the math" for their teacher, rather than see math as an opportunity for peer discussion, problem solving or reflection.

Here's the comment to my post that I received from "Pjack." I'm glad to see that at least one student is reflecting on his progress as a learner. (for more on student reflection see my post on the Reflective Student)

"The way math is taught is can be somewhat disheartening in many cases, as illustrated by that kid's drawing. As a high school student, and one who isn't that great with numbers (art kid here), one of my favorite classes I've ever taken, of all the most unlikely things, was summer school physics. The teacher did a brief lecture, gave us some formulas for how to calculate this and that, put us in groups of our choosing, had us figure out one problem per group in a collaborative fashion, and then present the answer to the class, whether it was right or wrong. The class would then give constructive feedback, and ask us questions, which we would work as a class to answer. The teacher sat at his desk the entire time, willing to offer help to those that asked but otherwise removed. The thing he repeated was, "What you put in to it you get out of it." Needless to say, it was an interesting experience, and one of the first times I did math collaboratively. Sadly, many of the students (soph/juniors in high school) made comments like, "He doesn't teach!" or were generally terrified of this responsibility. Really goes to show how little we feel prepared to take control over our own learning, at times. I notice this sort of teacher-dependency in some amount in almost every class."

Hi Peter,
I wish to increase my grade 3 and 4 students to reflect on their math problem solving processes.
Looking for interesting prompts to get their self-reflection into a written and/or oral response.
Any suggestions or sites to visit?
Thanks,
Petr Hejny

I think that’s an important part of “behaving” like a mathematician – being able to express your thinking to someone else. Not only do students come to better understand what they did. But they also need to think about their audience (fellow students) and what they will need to understand the process and logic. Thus the act of having them teach each other serves as a great prompt.